**3. Fluid-solid phase transition of self-assembled Lipid A-diphosphate cluster**

By applying freeze-fracture electron microscopy and X-ray diffraction techniques a qualitative phase relationship of Lipid A-diphosphate has been reported [32, 33]. These results were taken from samples of Lipid A extracted from Salmonella Minnesota, E. coli rough mutant LPS and from Salmonella enterica serovar Minnesota. In their qualitative study the aqueous specimens have been examined in the presence of mM phosphate buffers by synchrotron radiation and analyzed by their diffraction profiles e.g. cubic, hexagonal or simple cubic structures. However, there ionic strength was a magnitude higher than the one used for preparing electrostatically stabilized Lipid A-diphosphate dispersions with *I* = 10-4 to 10-6 M [12]. Especially, SAXD and SAXS are very suitable to characterize the 3-d structure or ordering in solution of the self-assembled Lipid A-phosphate clusters and probe their corresponding long-range order parameters. For comparison with light scattering, the most important advantage of the applied X-rays is their low refractive index contrast (the difference in index of refraction is of the order of 10-6), so the occurrence of multiple scattering and incoherent background scattering is significantly reduced and a much wider range of scattering vectors are available. It was observed that upon reaching a nanocluster size of 500 – 600 nm the suspensions became iridescent to visible light: thus, the iridescence acts as a visual marker of nanocluster size. Recently, the iridescent solutions have been physically analyzed and interpreted in terms of mass, surface charge, size and shape. The influence of polydispersity in charge, size and mass has been elucidated and included in all further experiments and simulations [7-13]. The most compelling observations of the colloidal crystallization and also of Lipid A-diphosphates in aqueous solutions at very low ionic strength conditions ( 10-6 M) are the order-disorder transition and the structural transition from a body-centered cubic (BCC) to a face-centered (FCC) structure [34, 35]. In these dispersions it is essential to consider the co-occurrence of phase separation and crystalline ordering, where it has been suggested that the crystalline phase is a supercooled liquid phase with some liquid retained in a metastabile state for a certain period of time, even at 0.58. Experimental phase diagrams of Lipid A-diphosphate dispersions in NaCl or NaOH as shown in Fig. 2 are very helpful in searching for crystal formation, order– disorder as a function of ionic strength *I*, *n* and T. Moreover, they are useful for comparison with the theoretical predictions [36, 37]. Normally the crystalline arrays form spontaneously through self-assembly of charged colloidal Lipid A-phosphate spheres in low ionic strength but at low polydispersity in size, mass and charge. The spontaneous formation of selfassembled Lipid A-diphosphate crystallization is mainly driven by the excluded-volume entropy. The decrease in entropy in the colloidal crystals is associated with a nonuniform mean density, however, a greater local volume that each particle can independently explore compensates for these phenomena. If the amount of base (cs) were increased, a new fluid reentrant disordered phase of self-assembled Lipid A-diphosphate clusters was encountered followed by a fluid ordered-crystalline BCC phase for low *n* when using NaOH as an electrolyte in the crystallization process.

#### **3.1. Freezing and melting**

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**cluster** 

protection of CAMP synthesis and sustaining remissions. The chemical structure of the proinflammatory component of *LPS,* Lipid A (Fig. 1), varies between bacteria of different

**3. Fluid-solid phase transition of self-assembled Lipid A-diphosphate** 

By applying freeze-fracture electron microscopy and X-ray diffraction techniques a qualitative phase relationship of Lipid A-diphosphate has been reported [32, 33]. These results were taken from samples of Lipid A extracted from Salmonella Minnesota, E. coli rough mutant LPS and from Salmonella enterica serovar Minnesota. In their qualitative study the aqueous specimens have been examined in the presence of mM phosphate buffers by synchrotron radiation and analyzed by their diffraction profiles e.g. cubic, hexagonal or simple cubic structures. However, there ionic strength was a magnitude higher than the one used for preparing electrostatically stabilized Lipid A-diphosphate dispersions with *I* = 10-4 to 10-6 M [12]. Especially, SAXD and SAXS are very suitable to characterize the 3-d structure or ordering in solution of the self-assembled Lipid A-phosphate clusters and probe their corresponding long-range order parameters. For comparison with light scattering, the most important advantage of the applied X-rays is their low refractive index contrast (the difference in index of refraction is of the order of 10-6), so the occurrence of multiple scattering and incoherent background scattering is significantly reduced and a much wider range of scattering vectors are available. It was observed that upon reaching a nanocluster size of 500 – 600 nm the suspensions became iridescent to visible light: thus, the iridescence acts as a visual marker of nanocluster size. Recently, the iridescent solutions have been physically analyzed and interpreted in terms of mass, surface charge, size and shape. The influence of polydispersity in charge, size and mass has been elucidated and included in all further experiments and simulations [7-13]. The most compelling observations of the colloidal crystallization and also of Lipid A-diphosphates in aqueous solutions at very low ionic strength conditions ( 10-6 M) are the order-disorder transition and the structural transition from a body-centered cubic (BCC) to a face-centered (FCC) structure [34, 35]. In these dispersions it is essential to consider the co-occurrence of phase separation and crystalline ordering, where it has been suggested that the crystalline phase is a supercooled liquid phase with some liquid retained in a metastabile state for a certain period of time, even at 0.58. Experimental phase diagrams of Lipid A-diphosphate dispersions in NaCl or NaOH as shown in Fig. 2 are very helpful in searching for crystal formation, order– disorder as a function of ionic strength *I*, *n* and T. Moreover, they are useful for comparison with the theoretical predictions [36, 37]. Normally the crystalline arrays form spontaneously through self-assembly of charged colloidal Lipid A-phosphate spheres in low ionic strength but at low polydispersity in size, mass and charge. The spontaneous formation of selfassembled Lipid A-diphosphate crystallization is mainly driven by the excluded-volume entropy. The decrease in entropy in the colloidal crystals is associated with a nonuniform mean density, however, a greater local volume that each particle can independently explore compensates for these phenomena. If the amount of base (cs) were increased, a new fluid re-

species where the Gram-negative bacteria modulate the structure of their *LPS*.

It was possible to prepare stable aqueous colloidal dispersions of Lipid A-diphosphate and their approximants with low polydispersity in shape, size, and charge over a discrete range of volume fraction, [9-11]. The phase transitions were a correlated liquid phase, a cubic FCC and a body-centered cubic crystalline phase [35]. These phases were detected in the presence of mM NaCl for different volume fractions, ; and various crystal forms (BCC and FCC) could be obtained. It was found that these assemblies were consistent with an assembly for a BCC lattice (*Im3m*) with *a* = 35.5 nm. However, a mixture of equimolar concentrations of the two antagonistic molecules revealed a SAXS-powder diffraction pattern a light scattering profile for crystals of sizes of 1 m that could be indexed for a much larger face-centered (*Fd3m)* unit cell, with *a* = 58.0 nm. However, when employing the similar conditions for colloidal Lipid A-diphosphate dispersions but through addition of M NaOH rather than by removing NaCl [35] a very different phase behavior was observed (Fig. 2). By varying the amount of added NaOH (or NaCl) it was possible to determine the effective charge, *Zeff* for various *n* values and the screening parameter, *k,* for the excess electrolyte (cs). For sufficiently large values of *n*, Lipid A-diphosphate crystallized through an increase in *Zeff* at a constant cS when adding M NaOH. When the cs were increased, the crystals melted with little change in *Zeff* . An increase in the cS enhanced interparticle interaction and attraction due to many-body effects (NaOH), but influences long-range interactions where particles repel one another at large separation distances in the presence of NaCl; thus repulsion increases with decreasing particle-particle separation and decreasing ionic strength. The effective charge and *k = 4 kBTB (n Zeff + 2 103/NAcse)1/2*, with B = 0.735 nm*,* the Debye screening length, account for counterion condensation and many-body effects. - If the effective charge determined from scattering measurements was used in the simulations, the equilibrium phase boundaries were consistent with predicted universal melting-line simulations [36, 37]. It seems that the presence of NaOH in the aqueous dispersions of Lipid A-diphosphate stabilized a twostate structure. The stabilizing effect was promoted by long-range (counter-ion mediated) attractive interactions between the crystalline clusters and the many-body effects. This Lipid A-diphosphate cluster is able to undergo both a fluid-order and an order-fluid transition.

When the NaOH concentration and the particle-number density of Lipid A-diphosphate is increased, the length scale of the repulsion decreased, because of many-body effects and the disorder-order-transition occurred at a particle-number density close to the freezing transition. When the NaOH concentration and the particle-number density of Lipid Adiphosphate is increased, the length scale of the repulsion decreased, because of many-body effects and the disorder-order-transition occurred at a particle-number density close to the freezing transition. At lower particle-number densities, as the length scale of the repulsive forces increased, the fluid-crystalline transition gave rise to BCC-type crystals.

**Figure 2.** Experimental phase diagrams of self-assembled charged Lipid A-diphosphate and their approximants at constant temperature (T = 291 K) as a function of particle number density, *n*, and ionic strength (*I*). **(A)** Ordered crystal phases appeared after considerable reduction of (*I)* with a large Debye length (NaCl) due to a stabilized electrostatic repulsion between the various self-assembled Lipid Adiphosphate clusters: ▼ Lipid A-diphosphate (A in Fig. 1) crystals; ● self-assembled Lipid Adiphosphate clusters comprising of Lipid A-diphosphate (A) and (C) shown in Fig. 1; ■ self-assembly of Lipid A-diphosphate clusters with (A) and (B) components; ■ self-assembly of components B and C; ▼ self-assembly of component (A) with six chains & with two double chained Lipid A-diphosphate at the non-educing end of the disaccharide; ■ self-assembly of the Lipid A-diphosphate approximant C (Fig. 1). *Inset:* Single spherical Lipid A-diphosphate clusters with *d* = 70.0 nm (SEM image). They form because of low shape and charge polydispersity ( 10%). **(B)** Phase diagram of charged spherical Lipid A-diphosphate clusters with the same composition as in **(A),** however, in the presence of M NaOH**.** The re-entrant melting lines are shown at the left boundary (charging) and at the right boundary (screening), respectively. The two-phase regions are indicated as horizontal arrows. The red dotted lines indicate the equivalent titration points obtained from conductometric titrations. The**·●●●**lines are theoretical fits to the experimental data applying an effective charge of *eff Z* = 345 76 for the left boundary, for the right boundary at maximum interaction the effective charge was *eff Z* = 320 50. The corresponding values for NaCl (**A)** were *eff Z* = 470 61 and *eff Z* = 500 50, respectively. **Insets***:* An ordered hexagonal columnar phase of non-crystalline Lipid A-diphosphate in the aqueous dispersion (Fluid 2) in (B) at high M NaOH, contrary to (A)**.** Lipid A-diphosphate clusters of diameter *d* = 6.0 nm are only present in the Fluid 1 Phase (SEM image) in (B), whereas the Lipid A-clusters in the hexagonal Fluid Phase 2 exhibit a nearest neighbor distance of 35.1 nm and a packing fraction of 0.68.

This implies that self-screening was much smaller than in previous studies and very different for Lipid A-monophosphate phases [38]. The experimental observations and the simulation support the existence of a transition from a fluid to a BCC structure rather than to an expected FCC structure for Lipid A-diphosphate clusters in e.g 5.0 mM NaCl. However, there was no FCC structure present for a certain NaOH concentration, but there was a crystalline BCC phase present between two clearly defined fluid phases with no crystals. It was rather unusual to encounter BCC structures for ionic strengths of different magnitude (5.0 M NaCl vs. 50.0 M NaOH) and for the same *n*, therefore, the OH- ions must contribute to the scenario. It is also feasible that the structural transition path was influenced by topological dissimilarities but differently forms the corresponding Lipid Amonophosphate crystalline phase, because of altered elastic deformations between the crystalline BCC phase which formed and the fluid phases from which it originated. The nearest-neighbor interparticle distance, 2*dexp =* 2/Q110 = 32.2 nm was estimated from the experimental peak positions and compared with the average theoretical distance, 2 *dth* = 3/ <sup>3</sup> 4*n* , for various *n*, 20 m-3 ≤ *n* ≤ 400 m-3. For this limited particle-number density range the double-logarithmic plot of 2 *dexp* and 2 *dth* vs. *n* revealed a straight line with a slope of -0.32. The nearest-neighbor distance in the re-entrant fluid phase was determined as *dN-N =* 33.0 nm, surprisingly for all Lipid A-diphosphate clusters including those with different "subunits". The nearest-neighbor distance for the fluid phase before freezing was found to be *dN-N =* 32.2 nm. The nearest-neighbor distance for the crystalline phase revealed a value of *dN-N =* 30.8 nm. This value was expected to be smaller than the average interparticle distance 2*dth* = 32.2 nm when a homogeneous particle distribution was assumed with cubic bcc symmetry.

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freezing transition. At lower particle-number densities, as the length scale of the repulsive

**Figure 2.** Experimental phase diagrams of self-assembled charged Lipid A-diphosphate and their approximants at constant temperature (T = 291 K) as a function of particle number density, *n*, and ionic strength (*I*). **(A)** Ordered crystal phases appeared after considerable reduction of (*I)* with a large Debye length (NaCl) due to a stabilized electrostatic repulsion between the various self-assembled Lipid Adiphosphate clusters: ▼ Lipid A-diphosphate (A in Fig. 1) crystals; ● self-assembled Lipid A-

diphosphate clusters comprising of Lipid A-diphosphate (A) and (C) shown in Fig. 1; ■ self-assembly of Lipid A-diphosphate clusters with (A) and (B) components; ■ self-assembly of components B and C; ▼ self-assembly of component (A) with six chains & with two double chained Lipid A-diphosphate at the non-educing end of the disaccharide; ■ self-assembly of the Lipid A-diphosphate approximant C (Fig. 1). *Inset:* Single spherical Lipid A-diphosphate clusters with *d* = 70.0 nm (SEM image). They form because of low shape and charge polydispersity ( 10%). **(B)** Phase diagram of charged spherical Lipid A-diphosphate clusters with the same composition as in **(A),** however, in the presence of M NaOH**.** The re-entrant melting lines are shown at the left boundary (charging) and at the right boundary (screening), respectively. The two-phase regions are indicated as horizontal arrows. The red dotted lines indicate the equivalent titration points obtained from conductometric titrations. The**·●●●**lines are theoretical fits to the experimental data applying an effective charge of *eff Z* = 345 76 for the left boundary, for the right boundary at maximum interaction the effective charge was *eff Z* = 320 50. The corresponding values for NaCl (**A)** were *eff Z* = 470 61 and *eff Z* = 500 50, respectively. **Insets***:* An ordered hexagonal columnar phase of non-crystalline Lipid A-diphosphate in the aqueous dispersion (Fluid 2) in (B) at high M NaOH, contrary to (A)**.** Lipid A-diphosphate clusters of diameter *d* = 6.0 nm are only present in the Fluid 1 Phase (SEM image) in (B), whereas the Lipid A-clusters in the hexagonal

Fluid Phase 2 exhibit a nearest neighbor distance of 35.1 nm and a packing fraction of 0.68.

This implies that self-screening was much smaller than in previous studies and very different for Lipid A-monophosphate phases [38]. The experimental observations and the simulation support the existence of a transition from a fluid to a BCC structure rather than to an expected FCC structure for Lipid A-diphosphate clusters in e.g 5.0 mM NaCl. However, there was no FCC structure present for a certain NaOH concentration, but there

forces increased, the fluid-crystalline transition gave rise to BCC-type crystals.

The observed intersphere spacing was normally close to the calculated mean sphere distance except at the interfacial region of the dispersions, where there was contact with the air or a wall. Melting is initiated when the amplitude of vibration becomes sufficiently large for the occurrence of partly shared occupancy between adjacent particles. It occurs when the root mean square of the vibration amplitude of a crystal exceeds a threshold value (~ 0.15 *dN-<sup>N</sup>*) according to Lindemann [39] and it would result in a movement of ~ 6.0 nm, which is a distance significantly smaller than the spacing between the surfaces of any of the spherical colloidal Lipid A-diphosphate clusters and a distance much less than the screening length. The Lindemann rule does not hold for crystals in 2d which have quasi-long-range instead of long-range translational order [40]. Measurements of the short-time and the long-time diffusion constants by quasi-elastic light scattering yielded a ratio of ~ 11 in the freezing region for the Lipid A-diphosphate cluster [41]. Furthermore, the possibility exists that the charge deduced from the melting line was also essential to center the particle within the cubic BCC unit cell. *Note*: According to the rule of Verlet and Hansen [42], crystallization occurs when the structure factor of ordinary liquids exceeds a value of 2.85 for 3d and 4 in 2d. Furthermore, when plotted S(Q) and *n* on a double-log graph a value of *df* = 1.75 was obtained, where S(Q) is the effective structure factor, Q is the scattering vector, *df* is the fractal dimension and close to the one found for a diffusion-limited cluster aggregation of 1.80.

This result may explain why the Lipid A-diphosphate basic arrays adopted the form of colloidal clusters at low particle-number densities and low NaOH concentrations. The number of seeding Lipid A-diphosphate clusters of *d* = 7 nm required to form a fractal nucleus of a given size was considerably lower than the number required for a compact nucleus. These parameters determined whether or not small clusters or sub-critical nuclei developed. Once formed, further cluster growth took place if a sufficient supply of Lipid A-diphosphate clusters of *d* = 7 nm were available. Therefore, cluster growth depended upon *n*, the size and the charge polydispersity and the availability of residual Lipid A-diphosphate clusters. A further increase in the NaOH concentration resulted in crystal melting and a re-entry into the fluid phase. The morphology of the clusters detected in such dispersions was similar to those of the Lipid A-diphosphate clusters observed before freezing took place. At a sufficiently high concentration of M NaOH, where strong interactions occurred, freezing can take place and a two-phase region was formed. If the M NaOH was increased there was an increase in charge on the selfassembled Lipid A-diphosphate clusters according to R–H2PO4H + OH- R–HPO4- + H2O. At low M NaOH, the Lipid A-diphosphate clusters retained their BCC structure. With additional increases in the M NaOH the interactions became screened with neither an increase nor a decrease in charge and the system began to melt. Although the Lipid Adiphosphate samples investigated covered a limited pH-range (4.5 pH 7.5), there was a sufficient excess of NaOH to attribute the re-entrant occurrence to added screening produced by the excess. This is completed different form the situation using NaCl. Because of the Lipid A-diphosphate cluster counterions, the screening parameter, increased steadily if *n*-1/3 remained constant. As a result, a decrease in the equilibriumstate lines will be observed and the melting line was crossed. This accounted for the maximum interaction equilibrium state line when the surface charges approached their highest value. Consequently, any further addition of M NaOH screened the Lipid Adiphosphate particle surface charge and initiated a reduction in the cluster-cluster interaction. The screening parameter, , then depended only on the screening electrolyte (NaOH or NaCl). The result was an increase in the equilibrium state lines which again crossed the melting line.

#### **3.2. BCC and FCC structures of Lipid A-phosphates**

Some new crystalline Lipid A-diphosphate clusters and their approximants have been developed since the protocol for obtaining electrostatically stabilized solutions of Lipid A-diphosphates or for the corresponding monophosphates at various *n* was available [11-13]. The well-ordered Lipid A-diphosphate clusters and the presence of higher order diffraction peaks corroborated the existence of crystalline Lipid A-diphosphate material documented for the BCC and FCC structures assigned to the space groups *Im* 3 *m* & *Fd* 3 *m* [43] depicted in Figs 3 and 4. It was observed that the (211) peak at cS = 3.15 M NaOH and the height of this reflection increased with *n* holding cB constant (Fig. 3). In addition the sensitivity of Lipid A-diphosphate clusters on pH is illustrated in Fig. 5B. The absence of the specific reflections (Figs. 3B, 4 & 5) of the X-ray diffraction patterns and small-area electron diffraction pattern reinforced the argument that the lattice type was face-centered cubic, therefore, two space groups were possible, namely *Fd* 3 and *Fd* 3 *m*.

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crossed the melting line.

*Fd* 3 *m*.

**3.2. BCC and FCC structures of Lipid A-phosphates** 

nucleus. These parameters determined whether or not small clusters or sub-critical nuclei developed. Once formed, further cluster growth took place if a sufficient supply of Lipid A-diphosphate clusters of *d* = 7 nm were available. Therefore, cluster growth depended upon *n*, the size and the charge polydispersity and the availability of residual Lipid A-diphosphate clusters. A further increase in the NaOH concentration resulted in crystal melting and a re-entry into the fluid phase. The morphology of the clusters detected in such dispersions was similar to those of the Lipid A-diphosphate clusters observed before freezing took place. At a sufficiently high concentration of M NaOH, where strong interactions occurred, freezing can take place and a two-phase region was formed. If the M NaOH was increased there was an increase in charge on the selfassembled Lipid A-diphosphate clusters according to R–H2PO4H + OH- R–HPO4-

H2O. At low M NaOH, the Lipid A-diphosphate clusters retained their BCC structure. With additional increases in the M NaOH the interactions became screened with neither an increase nor a decrease in charge and the system began to melt. Although the Lipid Adiphosphate samples investigated covered a limited pH-range (4.5 pH 7.5), there was a sufficient excess of NaOH to attribute the re-entrant occurrence to added screening produced by the excess. This is completed different form the situation using NaCl. Because of the Lipid A-diphosphate cluster counterions, the screening parameter, increased steadily if *n*-1/3 remained constant. As a result, a decrease in the equilibriumstate lines will be observed and the melting line was crossed. This accounted for the maximum interaction equilibrium state line when the surface charges approached their highest value. Consequently, any further addition of M NaOH screened the Lipid Adiphosphate particle surface charge and initiated a reduction in the cluster-cluster interaction. The screening parameter, , then depended only on the screening electrolyte (NaOH or NaCl). The result was an increase in the equilibrium state lines which again

Some new crystalline Lipid A-diphosphate clusters and their approximants have been developed since the protocol for obtaining electrostatically stabilized solutions of Lipid A-diphosphates or for the corresponding monophosphates at various *n* was available [11-13]. The well-ordered Lipid A-diphosphate clusters and the presence of higher order diffraction peaks corroborated the existence of crystalline Lipid A-diphosphate material documented for the BCC and FCC structures assigned to the space groups *Im* 3 *m* & *Fd* 3 *m* [43] depicted in Figs 3 and 4. It was observed that the (211) peak at cS = 3.15 M NaOH and the height of this reflection increased with *n* holding cB constant (Fig. 3). In addition the sensitivity of Lipid A-diphosphate clusters on pH is illustrated in Fig. 5B. The absence of the specific reflections (Figs. 3B, 4 & 5) of the X-ray diffraction patterns and small-area electron diffraction pattern reinforced the argument that the lattice type was face-centered cubic, therefore, two space groups were possible, namely *Fd* 3 and

+

**Figure 3.** (**A**) SAXS profiles I(Q) vs. Q, with Q = (4/)sin/2), of BCC type colloidal crystals ( = 1.54 nm) with a = 37.6 nm composed of Lipid A-diphosphate and "subunit" C (Fig. 1) . The assigned space group was *Im3m*, origin at center m3m, and equivalent positions 0, ½, ½; ½, 0, ½; ½, ½, 0 (*Q229*) based on the molecular composition and the assumed spherical diameter of *d* = 7.0 nm which was consistent with form-factor scattering at higher Q. The black dotted scattering profile is for the Lipid A-diphosphate phase at = 3.5 x 10-4, *I* = 0.5 mM NaCl, the solid-red line is the profile for an equimolar mixture of the antagonistic molecule depicted in B of Figure 1 for Lipid A-diphosphate with *a* = 35.5 nm. (**B**) SAXS profiles of colloidal crystals of the FCC type (*Fd* 3 *m*), the black-dotted line corresponds to Lipid Adiphosphate with *a* = 57.5 nm comprising of the components A and B (Fig. 1). The red-solid line is for the colloidal mixture of Lipid A-diphosphate and antagonistic Lipid A-diphosphate [47] (Fig. 1B) both are at = 5.4 x 10-4, I = 0.5 mM NaCl. The green solid SAXS profile represents the results from a mixture of Lipid A-diphosphate with the corresponding monosaccharide of Lipid A-diphosphate at = 3.4 x 10-4, I = 0.5 mM NaCl. **Insets:** Crystal morphologies as they appear in SEM images and simulated with the *Accelrys Software Materials Studio 4.4 Module Morphology Version 6.0,* San Diego (USA). The corresponding TEM images are shown in (C) and (D); the scale bar is 10 nm; (D) illustrates the chemical structure of the antagonistic Lipid A-diphosphate [47] composed only of a diphosphorylated glucosamine residue and two fatty-acid chains.

The two space groups were also centrosymmetric and belong to the Laue classes *m* 3 and *m* 3 *m*. *Note: Fd* 3 *m* corresponds to special positions of *Fd* 3 . The observed and calculated *hkl*  sets of Bragg reflections were consistent with a combination of different sites in the *Pm* 3 *n* (*a* and *d*), or of sites *a* and *d* in the *Fd* 3 *m* (Fig. 5). High-resolution transmission electron microscopy, SAED on crystalline Lipid A-diphosphate rods of the order of 2-3 m in length and diameters of several nm obtained at pH 8.0 [45] revealed that the rods were held to the truncated polyhedra with a five-fold symmetry (Fig. 6).

**Figure 4. (A)** S(Q) vs. Q profile for colloidal FCC-type crystals of Lipid A-diphosphate clusters with *a* = 57.0 nm for *n* = 140 m-3 and cS = 2.05 M NaOH. The lower curve (---) reveals the differences between observed () and calculated (**─)** intensities of the refined parameters form Rietveld analysis and X-ray powder diffraction pattern (*Fd* 3 *m*, site: 8a: 1/8, 1/8, 1/8 and 16-hedra: site 16d: ½, ½, ½, 12-hedra). **(B)** An SEM image is shown of m sized single crystals (bar scale ≈1.0 m) and the overall morphology of this crystal type and the Miller indexed faces are shown in (C).

By using computer simulations with multi-slice calculations, the Lipid A-diphosphate structure was obtained. The image multi-slice image simulations were carried out for the 100kV TEM Joel Microscope (T 3010) with imaging facilities for hollow-cone illuminations and using the Cowley algorithm [46, 47]. In addition, after successful indexing of the X-ray diffraction profiles and the selected area diffraction pattern (SAED), after the successful indexing of the powder-diffraction patterns and the selected-area diffraction patterns, a Pawley refinement was performed, taking the following parameters into consideration: cell parameters, peak-profile parameters, background and zero shifts. Following this refinement, a structure solution was imitated using a direct-space Monte Carlo-simulated annealing approach and a full-profile comparison was implemented. By employing a global optimization algorithm, trial structures were continuously generated by modifications in the specified degrees of freedom, i.e. three translations, three rotations and the dihedral angles.

It was possible to show that most of the Lipid A-diphosphate particles were orientated in the [001] direction with respect to the substrate for one of the five deformed tetrahedral subunits, i.e., the fivefold axis was parallel to the surface of the substrate [48]. Due to the presence of Lipid A-diphosphate and the surface tension, the only growth in the direction of the fivefold axis of decahedra was possible, resulting in long rods.

Since *n* = *n\** (*n\** = particle/length3) the orientational entropy and the electrostatic repulsion of the free energy expression for these charged rods favor antiparallel alignment of the rods [45], this will give rise to a cubic lattice-like interparticle structures as noticed in Figure 5**(C).** For *n n\** and 10 M NaOH a hexagonal packing of parallel rods can be anticipated as an appropriate description. If one considers the correlation of nearestneighbor rods of Lipid A –diphosphate, then a parallel alignment of nearest neighbor rods is observed with a local ordering parameter S = 0.07 at *n* = 2.8 *n\**. Individual rod-shaped particles are noticed in Figure 5B whereas in Figure 5A N-regions of Lipid A-diphosphate particles are observed, where the particles exhibit parallel orientations, which may correspond to Sm precursors. When *n* is significantly increased, the Lipid A-diphosphate clusters grow laterally, their contours become clearer, and more layering of the clusters appear. The particle packing fraction *<sup>P</sup>* for the Sm phase was estimated to 0.28. The Sm layer period and in-layer separation were calculated to be 2.8 and 2.4 nm, respectively, for *n* = 5.5 *n\**.

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the dihedral angles.

**Figure 4. (A)** S(Q) vs. Q profile for colloidal FCC-type crystals of Lipid A-diphosphate clusters with *a* = 57.0 nm for *n* = 140 m-3 and cS = 2.05 M NaOH. The lower curve (---) reveals the differences between observed () and calculated (**─)** intensities of the refined parameters form Rietveld analysis and X-ray powder diffraction pattern (*Fd* 3 *m*, site: 8a: 1/8, 1/8, 1/8 and 16-hedra: site 16d: ½, ½, ½, 12-hedra). **(B)** An SEM image is shown of m sized single crystals (bar scale ≈1.0 m) and the overall morphology

By using computer simulations with multi-slice calculations, the Lipid A-diphosphate structure was obtained. The image multi-slice image simulations were carried out for the 100kV TEM Joel Microscope (T 3010) with imaging facilities for hollow-cone illuminations and using the Cowley algorithm [46, 47]. In addition, after successful indexing of the X-ray diffraction profiles and the selected area diffraction pattern (SAED), after the successful indexing of the powder-diffraction patterns and the selected-area diffraction patterns, a Pawley refinement was performed, taking the following parameters into consideration: cell parameters, peak-profile parameters, background and zero shifts. Following this refinement, a structure solution was imitated using a direct-space Monte Carlo-simulated annealing approach and a full-profile comparison was implemented. By employing a global optimization algorithm, trial structures were continuously generated by modifications in the specified degrees of freedom, i.e. three translations, three rotations and

It was possible to show that most of the Lipid A-diphosphate particles were orientated in the [001] direction with respect to the substrate for one of the five deformed tetrahedral subunits, i.e., the fivefold axis was parallel to the surface of the substrate [48]. Due to the presence of Lipid A-diphosphate and the surface tension, the only growth in the direction of

Since *n* = *n\** (*n\** = particle/length3) the orientational entropy and the electrostatic repulsion of the free energy expression for these charged rods favor antiparallel alignment of the rods [45], this will give rise to a cubic lattice-like interparticle structures as noticed in Figure 5**(C).** For *n n\** and 10 M NaOH a hexagonal packing of parallel rods can be

the fivefold axis of decahedra was possible, resulting in long rods.

of this crystal type and the Miller indexed faces are shown in (C).

**Figure 5. (A)** S(Q) vs. Q profile for colloidal FCC-type crystals with *a* = 57.0 nm for *n* = 140 m-3 and cS = 2.05 M NaOH. The lower curve (---) reveals the differences between observed () and calculated (▬**)** intensities of the refined parameters. The inset depicts a SEM image of single crystals (size ≈1.0 m) and the morphology of this crystal type. **(B)** S(Q) vs. Q profiles as a function of *n* obtained by static light scattering for rods (▬) and SAXS (▬) at cs = 7.6 M NaOH, pH 7.85. These materials do not exhibit any iridescence. The dotted lines (**---**) represent the calculated S(Q) values for an isotropic solution of rods with *L* = 800 nm and *d* = 5.6 nm as a function of *n*; (·····) for a calculated dodecahedral Lipid Adiphosphate rod-model for *n* = 40 m-3 (T = 295 K). **(C)** shows a high resolution electron micrograph (HTEM) image of highly ordered and crystalline Lipid A-diphosphate nanorods in the [100] direction observed at pH 7.85 approaching the melting line for *n* = 55 m-3 (T = 295 K), the scale bar is 100 nm. **(D**) shows a HRTEM image of Lipid A-diphosphate observed at pH 7.85, crossing the melting line for *n* = 55 m-3 (T = 295 K), and at 5 M NaOH. The scale bar is also 100 nm.
